units

PHS3142

Faculty of Science

18 September 2017
08 March 2021

This unit entry is for students who completed this unit in 2014 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered, or view unit timetables.

Level | Undergraduate |

Faculty | Faculty of Science |

Organisational Unit | School of Physics |

Offered | Clayton Second semester 2014 (Day) |

Coordinator(s) | Dr Alexis Bishop |

This unit provides part of a major in theoretical physics. It consists of two 12-lecture sub-units, Advanced Quantum Mechanics and Computational Physics and a 12-hour seminar sub-unit. The key areas of study are:

- Advanced Quantum Mechanics: spin angular momentum, perturbation theory, scattering theory and the quantum theory of radiation;
- Computational Physics: discrete arrays to model the space and time evolution of functions or physical systems; a hands-on approach is used throughout to develop confidence and competency in using a computer to solve physical problems; includes a computer based assignment and short computational physics project; and
- Theoretical Seminar: seminar participation in theoretical problems, projects and presentations.

On completion of this unit students will be able to:

- Recall fundamental concepts from the sub-unit of Advanced Quantum Mechanics, which include Approximate Methods in Quantum Mechanics I: stationary (time-independent) perturbation theory, first and second order perturbation of a non-degenerate state, Higher order perturbation theory, Perturbation of a degenerate state and applications in atomic and nuclear physics, Time-dependent perturbation theory, Fermi's golden rule, The Ritz variational method, Semi-classical (WKB) approximation, Scattering Theory, Stationary scattering states, The Born approximation, Partial wave expansions, Phase shifts, Scattering of identical particles, The optical theorem, Introduction to Green function techniques, Charged Particles in an Electromagnetic Field, Gauge potentials and the electromagnetic field, Hamiltonian of a particle in an electromagnetic field, The Quantum Theory of Radiation and the interaction of radiation with atomic systems, Transition rates , Multipole transitions. Quantum electrodynamics, Geometric phases in quantum mechanics, Berry's phase, The Aharonov-Bohm effect, Path Integrals, and Free space propagator;

- Use a high level computer language such as Matlab to solve computation problems, and model systems, applicable to theoretical physics which include Numerical differentiation and integration, Finding roots, Special functions, Change of basis, Reduction to dimensionless forms, Discretization of quantum mechanical operators, Stationary and time-dependent Schrodinger equation, 1D scattering, Quantum harmonic oscillator, Eigenvalue problems, Bose-Einstein condensation and the Gross-Pitaevskii equation, Quantized vortices, Stochastic methods, Pseudo-random numbers, Monte Carlo method, Metropolis algorithm, 2D Ising model, Signal and Image Processing using the DFT and FFT, Convolution theorem, Filtering in 1D and 2D, Non-linear filtering and mathematical morphology, and Radon transform and tomography;

- Solve new problems in physics related to the core concepts of the unit by drawing on the theoretical underpinnings that illustrate the physics;

- Research topics in contemporary physics, and present critically assessed summaries as scientific reports and visual presentations;

- Apply educated reasoning to provide approximate solutions to scientific questions and advanced problems (Fermi questions).

Examination (2 hours): 23%

Assignments and computational projects: 43%

Seminar contributions: 34%

An average of 2 hours lectures, one 1-hour tutorial and one 1-hour seminar per week